scholarly journals Seismic Interferometry from Correlated Noise Sources

2021 ◽  
Vol 13 (14) ◽  
pp. 2703
Author(s):  
Daniella Ayala-Garcia ◽  
Andrew Curtis ◽  
Michal Branicki
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Ocean Waves ◽  
Seismic Interferometry ◽  
Correlated Noise ◽  
Highway Traffic ◽  
Noise Sources ◽  
Estimation Errors ◽  
Band Limited

It is a well-established principle that cross-correlating seismic observations at different receiver locations can yield estimates of band-limited inter-receiver Green’s functions. This principle, known as Green’s function retrieval or seismic interferometry, is a powerful technique that can transform noise into signals which enable remote interrogation and imaging of the Earth’s subsurface. In practice it is often necessary and even desirable to rely on noise already present in the environment. Theory that underpins many applications of ambient noise interferometry assumes that the sources of noise are uncorrelated in time. However, many real-world noise sources such as trains, highway traffic and ocean waves are inherently correlated in space and time, in direct contradiction to the these theoretical foundations. Applying standard interferometric techniques to recordings from correlated energy sources makes the Green’s function liable to estimation errors that so far have not been fully accounted for theoretically nor in practice. We show that these errors are significant for common noise sources, always perturbing or entirely obscuring the phase one wishes to retrieve. Our analysis explains why stacking may reduce the phase errors, but also shows that in commonly encountered circumstances stacking will not remediate the problem. This analytical insight allowed us to develop a novel workflow that significantly mitigates effects arising from the use of correlated noise sources. Our methodology can be used in conjunction with already existing approaches, and improves results from both correlated and uncorrelated ambient noise. Hence, we expect it to be widely applicable in ambient noise studies.

scholarly journals Seismic interferometry from correlated noise sources

2021 ◽  
Author(s):  
Daniella Ayala ◽  
Andrew Curtis ◽  
Michal Branicki
Keyword(s):  
Ambient Noise ◽  
Real Life ◽  
Seismic Energy ◽  
Seismic Interferometry ◽  
Correlated Noise ◽  
Highway Traffic ◽  
Noise Sources ◽  
Estimation Errors ◽  
Space And Time ◽  
Receiver Array

<p>It is a well-established principle that cross-correlating seismic observations at different receiver locations yields new seismic responses that, under certain conditions, provide a useful estimate of the Green's function between the given receiver locations (that is, the medium response at one receiver location, had there been an impulsive source located at the other receiver). This principle, known as seismic interferometry, is a powerful technique that transforms previously discarded data such as seismic codas or background noise into useful signals that allow us to remotely illuminate subsurface Earth structures.</p><p> </p><p>In practice it is often necessary and even desirable to rely on noise already present in the environment, since this type of seismic energy is freely and widely available in many regions around the globe.  Across many applications of ambient noise interferometry there exists a persistent assumption that the noise sources in question are uncorrelated in space and time, and that energy arrives at the receiver array more-less equally from all directions. That this assumption is so tenaciously made comes as no surprise since the underlying theory unambiguously requires that the noise sources be uncorrelated for interferometry to work.</p><p> </p><p>However, many real-world noise sources such as trains or highway traffic are inherently correlated both in space and time, in direct contradiction to these theoretical foundations. Violating the uncorrelatedness condition makes the Green’s function and associated phases liable to estimation errors that so far have not been accounted for. We show that these errors are indeed significant for commonly used noise sources, in some cases completely obscuring the phase one wishes to retrieve. Furthermore, we perform analysis that explains why stacking has the potential to reduce these errors in the interferometric estimate, as well as some limitations of this approach. This analytical insight allowed us to develop a novel workflow that mitigates or even completely removes the spurious effects arising from the use of correlated noise sources. Our methodology can be used in conjunction with already existing approaches, and hence we expect it to be widely applicable in real life ambient noise studies.</p>

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

scholarly journals Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A195-75A209 ◽  
Author(s):  
Kees Wapenaar ◽  
Deyan Draganov ◽  
Roel Snieder ◽  
Xander Campman ◽  
Arie Verdel
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Source Function ◽  
Stationary Points ◽  
Seismic Interferometry ◽  
Direct Wave ◽  
Reflected Wave

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the [Formula: see text]-axis, the crosscorrelation of the responses at two receivers along the [Formula: see text]-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transient (as in exploration seismology) or a noise signal (as in passive seismology), then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is theretrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surface-wave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

scholarly journals On the Green’s function emergence from interferometry of seismic wavefields generated in high-melt glaciers: implications for passive imaging and monitoring

2019 ◽  
Author(s):  
Amandine Sergeant ◽  
Malgorzata Chmiel ◽  
Fabian Lindner ◽  
Fabian Walter ◽  
Philippe Roux ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Seismic Anisotropy ◽  
Greenland Ice Sheet ◽  
Noise Sources ◽  
Processing Scheme ◽  
Seismic Scattering ◽  
Seismic Characterization ◽  
New Processing

Abstract. Ambient noise seismology has revolutionized seismic characterization of the Earth's crust from local to global scales. The elastic Green's function (GF) between two receivers can be reconstructed via cross-correlation of the ambient noise seismograms. An homogenized wavefield illuminating the propagation medium in all directions is a pre-requesite for obtaining accurate GF. For seismic data recorded on glaciers, this condition imposes strong limitations on GF convergence, because of minimal seismic scattering in homogeneous ice. We address this difficulty by investigating three patterns of seismic wavefields: a favourable distribution of icequakes and noise sources recorded on a dense array of 98 sensors on Glacier d'Argentière (France), a dominant noise source constituted by a moulin within a smaller seismic array on the Greenland ice-sheet, and crevasse-generated scattering at Gornergletscher (Switzerland). In Glacier d'Argentière, surface melt routing through englacial channels produces turbulent water flow creating sustained ambient seismic sources and thus favorable conditions for GF estimates. From the velocity measurements of reconstructed Rayleigh waves, we invert bed properties and depth profiles, and map seismic anisotropy, which is likely introduced by crevassing. In Greenland, we employ an advanced pre-processing scheme which include match-field processing and eigenspectral equalization of the cross-spectra to remove the moulin source signature and reduce the effect of inhomogeneous wavefields on the GF. At Gornergletscher, cross-correlations of icequake coda waves show evidence for homogenized wavefields. Optimization of coda correlation windows further promotes the GF convergence. This study presents new processing schemes on suitable array geometries for passive seismic imaging and monitoring of glaciers.

scholarly journals Studying CO2 storage with ambient-noise seismic interferometry: A combined numerical feasibility study and field-data example for Ketzin, Germany

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. Q1-Q13 ◽  
Author(s):  
Boris Boullenger ◽  
Arie Verdel ◽  
Bob Paap ◽  
Jan Thorbecke ◽  
Deyan Draganov
Keyword(s):  
Field Data ◽  
Ambient Noise ◽  
Co2 Storage ◽  
Time Lapse ◽  
Seismic Interferometry ◽  
Geologic Sequestration ◽  
Noise Sources ◽  
Noise Measurements ◽  
Band Limited ◽  
Geologic Setting

Seismic interferometry applied to ambient-noise measurements allows the retrieval of the seismic response between pairs of receivers. We studied ambient-noise seismic interferometry (ANSI) to retrieve time-lapse reflection responses from a reservoir during [Formula: see text] geologic sequestration, using the case of the experimental site of Ketzin, Germany. We applied ANSI to numerically modeled data to retrieve base and repeat reflection responses characterizing the impedances occurring at the reservoir both with and without the injection of [Formula: see text]. The modeled data represented global transmission responses from band-limited noise sources randomly triggered in space and time. We found that strong constraints on the spatial distribution of the passive sources were not required to retrieve the time-lapse signal as long as sufficient source-location repeatability was observed between the base and the repeat passive survey. To illustrate the potential of the technique, ANSI was applied to three days of passive field data recorded in 2012 at Ketzin. Comparison with the modeled results illustrated the potential to retrieve key reflection events using ANSI on field data from Ketzin. This study supports the idea that the geologic setting and characteristics of ambient noise at Ketzin may be opportune to monitor [Formula: see text] sequestration.

scholarly journals On the Green's function emergence from interferometry of seismic wave fields generated in high-melt glaciers: implications for passive imaging and monitoring

2020 ◽  
Vol 14 (3) ◽  
pp. 1139-1171 ◽  
Author(s):  
Amandine Sergeant ◽  
Małgorzata Chmiel ◽  
Fabian Lindner ◽  
Fabian Walter ◽  
Philippe Roux ◽  
...  
Keyword(s):  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Seismic Wave ◽  
Ambient Noise ◽  
Cross Correlation ◽  
Noise Sources ◽  
Wave Fields ◽  
Seismic Scattering ◽  
The Cross

Abstract. Ambient noise seismology has revolutionized seismic characterization of the Earth's crust from local to global scales. The estimate of Green's function (GF) between two receivers, representing the impulse response of elastic media, can be reconstructed via cross-correlation of the ambient noise seismograms. A homogenized wave field illuminating the propagation medium in all directions is a prerequisite for obtaining an accurate GF. For seismic data recorded on glaciers, this condition imposes strong limitations on GF convergence because of minimal seismic scattering in homogeneous ice and limitations in network coverage. We address this difficulty by investigating three patterns of seismic wave fields: a favorable distribution of icequakes and noise sources recorded on a dense array of 98 sensors on Glacier d'Argentière (France), a dominant noise source constituted by a moulin within a smaller seismic array on the Greenland Ice Sheet, and crevasse-generated scattering at Gornergletscher (Switzerland). In Glacier d'Argentière, surface melt routing through englacial channels produces turbulent water flow, creating sustained ambient seismic sources and thus favorable conditions for GF estimates. Analysis of the cross-correlation functions reveals non-equally distributed noise sources outside and within the recording network. The dense sampling of sensors allows for spatial averaging and accurate GF estimates when stacked on lines of receivers. The averaged GFs contain high-frequency (>30 Hz) direct and refracted P waves in addition to the fundamental mode of dispersive Rayleigh waves above 1 Hz. From seismic velocity measurements, we invert bed properties and depth profiles and map seismic anisotropy, which is likely introduced by crevassing. In Greenland, we employ an advanced preprocessing scheme which includes match-field processing and eigenspectral equalization of the cross spectra to remove the moulin source signature and reduce the effect of inhomogeneous wave fields on the GFs. At Gornergletscher, cross-correlations of icequake coda waves show evidence for homogenized incident directions of the scattered wave field. Optimization of coda correlation windows via a Bayesian inversion based on the GF cross coherency and symmetry further promotes the GF estimate convergence. This study presents new processing schemes on suitable array geometries for passive seismic imaging and monitoring of glaciers and ice sheets.

scholarly journals Green’s function representations for seismic interferometry

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI33-SI46 ◽  
Author(s):  
Kees Wapenaar ◽  
Jacob Fokkema
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Layered Medium ◽  
Closed Surface ◽  
Reciprocity Theorem ◽  
Stationary Points ◽  
Seismic Interferometry ◽  
Noise Sources ◽  
Shaping Filter ◽  
Reversal Invariance

The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh’s reciprocity theorem and the principle of time-reversal invariance that the acoustic Green’s function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green’s function. When a part of the enclosing surface is the earth’s free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green’s function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green’s functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

scholarly journals Directional balancing for seismic and general wavefield interferometry

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. SA1-SA14 ◽  
Author(s):  
Andrew Curtis ◽  
David Halliday
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Acoustic Scattering ◽  
Data Driven ◽  
Seismic Interferometry ◽  
Noise Sources ◽  
Naturally Occurring ◽  
Passive Seismic ◽  
Incoming Energy ◽  
Solid Bodies

In passive seismic interferometry using naturally occurring, heterogeneous noise sources and in active-source seismic interferometry where sources can usually only be distributed densely on the exterior of solid bodies, bias can be introduced in Green’s function estimates when amplitudes of energy have directional variations. We have developed an algorithm to remove bias in Green’s function estimates constructed using seismic interferometry when amplitudes of energy used have uncontrollable directional variations. The new algorithm consists of two parts: (1) a method to measure and adjust the amplitudes of physical, incoming energy using an array of receivers and (2) a method to predict and remove nonphysical energy that remains (and can be accentuated) in interferometrically derived Green’s functions after applying the method in step 1. To accomplish step 2, we have created two data-driven methods to predict the nonphysical energy using direct computation or move-out-based methods, and a way to suppress such energy using (in this case) helical least-squares filters. Two-dimensional acoustic scattering examples confirm the algorithm’s effectiveness.

scholarly journals Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A211-75A227 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob ◽  
Roel Snieder ◽  
Andrew Curtis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Bending Waves ◽  
Complex Source ◽  
Recent Developments ◽  
Diffusion Phenomena ◽  
Quantum Mechanical Scattering ◽  
Moving Media

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over differ-ent sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

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